A dichotomy for Borel functions

Abstract

The dichotomy discovered by Solecki in \cite{Sol} states that any Baire class 1 function is either $\sigma$-continuous or "includes" the Pawlikowski function $P$. The aim of this paper is to give an argument which is simpler than the original proof of Solecki and gives a stronger statement: a dichotomy for all Borel functions.